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Block #2,761,927

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2018, 5:58:10 PM Β· Difficulty 11.6543 Β· 4,081,565 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
92c31dc8db31e9398f5b97f513ad9c4e6d4cd748d7a5a569c4f863c00cb60820
View on Chainz β†—

Height

#2,761,927

Difficulty

11.654345

Transactions

1

Size

198 B

Version

2

Bits

0ba78329

Nonce

2,048,628,726

Timestamp

7/23/2018, 5:58:10 PM

Confirmations

4,081,565

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

2d1e719eda65af315b130555625b5ef3218cd6a87969720f76e9144654ab6cc7
Transactions (1)
Coinbase2d1e719eda65af…e9144654ab6cc7
1 in β†’ 1 out7.3500 XPM109 B
AZtxQr2F…7grUWrUz
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.

1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642749
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
1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.225 Γ— 10⁹³(94-digit number)
12254226150981751069…07731917056972642751
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
2.450 Γ— 10⁹³(94-digit number)
24508452301963502139…15463834113945285499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.450 Γ— 10⁹³(94-digit number)
24508452301963502139…15463834113945285501
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
4.901 Γ— 10⁹³(94-digit number)
49016904603927004278…30927668227890570999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.901 Γ— 10⁹³(94-digit number)
49016904603927004278…30927668227890571001
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
9.803 Γ— 10⁹³(94-digit number)
98033809207854008557…61855336455781141999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.803 Γ— 10⁹³(94-digit number)
98033809207854008557…61855336455781142001
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
1.960 Γ— 10⁹⁴(95-digit number)
19606761841570801711…23710672911562283999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.960 Γ— 10⁹⁴(95-digit number)
19606761841570801711…23710672911562284001
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
3.921 Γ— 10⁹⁴(95-digit number)
39213523683141603422…47421345823124567999
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:57,992,307 XPMΒ·at block #6,843,491 Β· updates every 60s
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