Block #317,587

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 7:33:28 PM · Difficulty 10.1513 · 6,492,600 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3ff007ca35ced9cd40062c998dbfac3c24792fc9f37e87c0074a27d3e389c0e

View on Chainz ↗

Height

#317,587

Difficulty

10.151256

Transactions

Size

968 B

Version

Bits

0a26b8b4

Nonce

77,475

Timestamp

12/17/2013, 7:33:28 PM

Confirmations

6,492,600

Mined by

⛏️ aRSAXA1reAhZ9UrngXnnSk2KEvAUNG6hPBmF8

Merkle Root

2e531c279e1c4f6b7abf15cb3decf0617a417717bc56bff8a61494dc81a3ea31

Transactions (1)

Coinbase2e531c279e1c4f…1494dc81a3ea31

1 in → 24 out9.6900 XPM879 B

AXA1reAh…G6hPBmF8 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AMiJebLB…rK2iN8iS

Prime Chain Origin

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

1.553 × 10⁹³(94-digit number)

15539954335887038025…83462510866695111169

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.553 × 10⁹³(94-digit number)

15539954335887038025…83462510866695111169

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.553 × 10⁹³(94-digit number)

15539954335887038025…83462510866695111171

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.107 × 10⁹³(94-digit number)

31079908671774076051…66925021733390222339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.107 × 10⁹³(94-digit number)

31079908671774076051…66925021733390222341

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.215 × 10⁹³(94-digit number)

62159817343548152102…33850043466780444679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.215 × 10⁹³(94-digit number)

62159817343548152102…33850043466780444681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.243 × 10⁹⁴(95-digit number)

12431963468709630420…67700086933560889359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.243 × 10⁹⁴(95-digit number)

12431963468709630420…67700086933560889361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.486 × 10⁹⁴(95-digit number)

24863926937419260840…35400173867121778719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.486 × 10⁹⁴(95-digit number)

24863926937419260840…35400173867121778721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #317,587

Cookie Preferences