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Block #1,350,380

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/2/2015, 12:20:48 AM Β· Difficulty 10.8022 Β· 5,455,864 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d5988bc7672d8830a9aacd05d7d70e7cb3fbb6cba0dfd0095505dbbdf5c35f06
View on Chainz β†—

Height

#1,350,380

Difficulty

10.802202

Transactions

2

Size

7.64 KB

Version

2

Bits

0acd5d1a

Nonce

1,021,390,709

Timestamp

12/2/2015, 12:20:48 AM

Confirmations

5,455,864

Mined by

⛏️ P2SHAQExeSJrWAjZrEpBJiBxYfxEEuVcKZ59La

Merkle Root

8aea47aae85b9974c083f5f4aceeed85b73910c35881a0856e85addd6b2e130b
Transactions (2)
Coinbase88696b5082d4ae…196004267aaa05
1 in β†’ 1 out8.6400 XPM109 B
AQExeSJr…VcKZ59La
f70d7769acf7c8…11b6cfc625301e
51 in β†’ 2 out23.2138 XPM7.44 KB
AWwfdq21…vNWPXG9RAbecWDS9…1vtToSML
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.

7.991 Γ— 10⁹⁡(96-digit number)
79919008944350212009…60829224072464253439
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
7.991 Γ— 10⁹⁡(96-digit number)
79919008944350212009…60829224072464253439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.991 Γ— 10⁹⁡(96-digit number)
79919008944350212009…60829224072464253441
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
1.598 Γ— 10⁹⁢(97-digit number)
15983801788870042401…21658448144928506879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.598 Γ— 10⁹⁢(97-digit number)
15983801788870042401…21658448144928506881
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
3.196 Γ— 10⁹⁢(97-digit number)
31967603577740084803…43316896289857013759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.196 Γ— 10⁹⁢(97-digit number)
31967603577740084803…43316896289857013761
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
6.393 Γ— 10⁹⁢(97-digit number)
63935207155480169607…86633792579714027519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.393 Γ— 10⁹⁢(97-digit number)
63935207155480169607…86633792579714027521
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
1.278 Γ— 10⁹⁷(98-digit number)
12787041431096033921…73267585159428055039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.278 Γ— 10⁹⁷(98-digit number)
12787041431096033921…73267585159428055041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,694,033 XPMΒ·at block #6,806,243 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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