Block #922,379

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:32:55 AM · Difficulty 10.9155 · 5,872,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c834225b71ac52acae3fd40c7237c6dcac7e95c0349d3d8cb8081f8b81ea5505

View on Chainz ↗

Height

#922,379

Difficulty

10.915536

Transactions

Size

115.99 KB

Version

Bits

0aea6095

Nonce

669,491,035

Timestamp

2/4/2015, 10:32:55 AM

Confirmations

5,872,793

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b12536852f69b2e14847bf67ec3498a684e2a0244c9940593cb5ca02fb23f496

Transactions (5)

Coinbasef02d50cfc1e943…17ff6fe83ae19c

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

644fd58fbe6630…fa07edda4638f1

200 in → 1 out1078.2012 XPM28.97 KB

AKuP4XsJ…owbodNxQ

84530f4f3bb837…907d684ea24011

200 in → 1 out1169.1428 XPM28.93 KB

AKuP4XsJ…owbodNxQ

093cb5bc0e4431…25468a1a432011

200 in → 1 out1025.0548 XPM28.94 KB

AKuP4XsJ…owbodNxQ

c2ee7221b14fc3…e0850de9211046

200 in → 1 out1072.4900 XPM28.95 KB

AKuP4XsJ…owbodNxQ

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.

1.041 × 10⁹⁷(98-digit number)

10411594888404123509…97594760016217983999

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

1.041 × 10⁹⁷(98-digit number)

10411594888404123509…97594760016217983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.041 × 10⁹⁷(98-digit number)

10411594888404123509…97594760016217984001

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

2.082 × 10⁹⁷(98-digit number)

20823189776808247018…95189520032435967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.082 × 10⁹⁷(98-digit number)

20823189776808247018…95189520032435968001

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

4.164 × 10⁹⁷(98-digit number)

41646379553616494036…90379040064871935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.164 × 10⁹⁷(98-digit number)

41646379553616494036…90379040064871936001

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

8.329 × 10⁹⁷(98-digit number)

83292759107232988072…80758080129743871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.329 × 10⁹⁷(98-digit number)

83292759107232988072…80758080129743872001

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

1.665 × 10⁹⁸(99-digit number)

16658551821446597614…61516160259487743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.665 × 10⁹⁸(99-digit number)

16658551821446597614…61516160259487744001

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