Block #917,374

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2015, 2:33:34 PM · Difficulty 10.9236 · 5,888,706 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fd79639e9b8dbf3ac3a3890b1b86a37a3f95ecd885a2896fdc9c35b61e9de9a

View on Chainz ↗

Height

#917,374

Difficulty

10.923580

Transactions

Size

3.82 KB

Version

Bits

0aec6fc1

Nonce

220,854,416

Timestamp

1/31/2015, 2:33:34 PM

Confirmations

5,888,706

Mined by

⛏️ P2SHAFvvbcKoxB3uycX7E9yVWrRrjen6Rfxr3F

Merkle Root

094a70b314cd4f678df6531995821e8e2515f2e8a9bdfc91b999d2d4f3e06a88

Transactions (5)

Coinbasebab4675414d2b5…91980fd8b60081

1 in → 1 out8.4300 XPM109 B

AFvvbcKo…n6Rfxr3F

ae9abde9848daf…1c9f85c1d8df01

6 in → 2 out71.1710 XPM968 B

AZFpfbVw…WE5cDbrh AYbQUuPy…ngBocWSr

1ac7736c95d190…067581b0622c60

4 in → 2 out31.2881 XPM670 B

AYbQUuPy…ngBocWSr AdeSrx4h…M2HRN1wU

0c2199ba63b31f…dca9f92b7acb5f

1 in → 2 out4.3400 XPM226 B

AJB9AK7s…jKt5NiMZ AHB3T3XQ…qv2EBTWC

f7fac2cb38554b…7cdef776d356af

12 in → 2 out4.0600 XPM1.81 KB

AVFsYE2Y…13BY7kWx AdGFnV3a…o6n2zX3x

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.

6.490 × 10⁹⁶(97-digit number)

64901513046165926862…26891660611682713599

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

6.490 × 10⁹⁶(97-digit number)

64901513046165926862…26891660611682713599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.490 × 10⁹⁶(97-digit number)

64901513046165926862…26891660611682713601

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

1.298 × 10⁹⁷(98-digit number)

12980302609233185372…53783321223365427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.298 × 10⁹⁷(98-digit number)

12980302609233185372…53783321223365427201

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

2.596 × 10⁹⁷(98-digit number)

25960605218466370744…07566642446730854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.596 × 10⁹⁷(98-digit number)

25960605218466370744…07566642446730854401

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

5.192 × 10⁹⁷(98-digit number)

51921210436932741489…15133284893461708799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.192 × 10⁹⁷(98-digit number)

51921210436932741489…15133284893461708801

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

1.038 × 10⁹⁸(99-digit number)

10384242087386548297…30266569786923417599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.038 × 10⁹⁸(99-digit number)

10384242087386548297…30266569786923417601

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