Block #613,640

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/3/2014, 4:52:47 AM · Difficulty 10.9329 · 6,191,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

977b54ee65965ff3bd0fa19883ee48a54435b4fabe82e6ce46aa6482c0b1371f

View on Chainz ↗

Height

#613,640

Difficulty

10.932851

Transactions

Size

527 B

Version

Bits

0aeecf56

Nonce

1,087,571,552

Timestamp

7/3/2014, 4:52:47 AM

Confirmations

6,191,504

Mined by

⛏️ `yxAH7s8DTYAadoFxjYcGJqTWgJSrna3f76ub

Merkle Root

7b701a5f8fce07c0add305330eccef3b8ecce63d9b236b7008e562d6131924f4

Transactions (1)

Coinbase7b701a5f8fce07…e562d6131924f4

1 in → 11 out8.3500 XPM437 B

AH7s8DTY…na3f76ub AbPcCMg4…719q6mAX AGz9gyZW…bo8NYQpw AXVLciVJ…uTVo9CdN ALkuF5Je…KBUB19wB

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.

5.370 × 10⁹³(94-digit number)

53704787778791824522…80125949716847148799

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

5.370 × 10⁹³(94-digit number)

53704787778791824522…80125949716847148799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.370 × 10⁹³(94-digit number)

53704787778791824522…80125949716847148801

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

1.074 × 10⁹⁴(95-digit number)

10740957555758364904…60251899433694297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.074 × 10⁹⁴(95-digit number)

10740957555758364904…60251899433694297601

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

2.148 × 10⁹⁴(95-digit number)

21481915111516729808…20503798867388595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.148 × 10⁹⁴(95-digit number)

21481915111516729808…20503798867388595201

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

4.296 × 10⁹⁴(95-digit number)

42963830223033459617…41007597734777190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.296 × 10⁹⁴(95-digit number)

42963830223033459617…41007597734777190401

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

8.592 × 10⁹⁴(95-digit number)

85927660446066919235…82015195469554380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.592 × 10⁹⁴(95-digit number)

85927660446066919235…82015195469554380801

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