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Block #885,340

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2015, 5:42:00 AM Β· Difficulty 10.9576 Β· 5,925,115 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
a826b249f555ca86cdc77725e1a8aaa135eddbaf7c13a17d6745fde25eae4fc3
View on Chainz β†—

Height

#885,340

Difficulty

10.957585

Transactions

3

Size

3.25 KB

Version

2

Bits

0af52452

Nonce

1,390,683,805

Timestamp

1/7/2015, 5:42:00 AM

Confirmations

5,925,115

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d550dc9133cf1a5238cc6f26eb1d2f1127fac15bcdb7b03bfa9951a192dd8da1
Transactions (3)
Coinbase91d47a9643ff37…9fd4d7da00aa28
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
7fe7aa29aa83e8…3cc36cfed96dc8
19 in β†’ 2 out28.1002 XPM2.82 KB
AQmP3XnU…T8TJgwBDAMvtubVd…o4DQF7AQ
df28c5f4ad6692…2967346840d5f5
1 in β†’ 2 out7.1287 XPM227 B
Ab5nariW…9aDqt8iFAT8meQ57…UWRhw19n
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.652 Γ— 10⁹⁡(96-digit number)
76522429470271768244…75879978262655916639
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.652 Γ— 10⁹⁡(96-digit number)
76522429470271768244…75879978262655916639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.652 Γ— 10⁹⁡(96-digit number)
76522429470271768244…75879978262655916641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁢(97-digit number)
15304485894054353648…51759956525311833279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.530 Γ— 10⁹⁢(97-digit number)
15304485894054353648…51759956525311833281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.060 Γ— 10⁹⁢(97-digit number)
30608971788108707297…03519913050623666559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.060 Γ— 10⁹⁢(97-digit number)
30608971788108707297…03519913050623666561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.121 Γ— 10⁹⁢(97-digit number)
61217943576217414595…07039826101247333119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.121 Γ— 10⁹⁢(97-digit number)
61217943576217414595…07039826101247333121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁷(98-digit number)
12243588715243482919…14079652202494666239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.224 Γ— 10⁹⁷(98-digit number)
12243588715243482919…14079652202494666241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁷(98-digit number)
24487177430486965838…28159304404989332479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,727,726 XPMΒ·at block #6,810,454 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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