Block #922,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:49:12 AM · Difficulty 10.9155 · 5,888,043 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a8646bad0018003a6bc098f6a9135c418e7ca503f0dae6b1f061e51ee92f9a0

View on Chainz ↗

Height

#922,392

Difficulty

10.915474

Transactions

Size

116.01 KB

Version

Bits

0aea5c82

Nonce

113,544,038

Timestamp

2/4/2015, 10:49:12 AM

Confirmations

5,888,043

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c369d0f2b37d1bc48f7d5d3882474b1a333a63ffd928857dec149bbfa890ce1f

Transactions (5)

Coinbase4402fc96e51b3a…b896f098ed1d5e

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

4b4783d5547625…3ec71a569f6767

200 in → 1 out1217.5886 XPM28.96 KB

AKuP4XsJ…owbodNxQ

497f8d7bef7aa2…4be84158869602

200 in → 1 out862.8775 XPM28.94 KB

AKuP4XsJ…owbodNxQ

6e0414ce1e239e…8a76db92f6de6d

200 in → 1 out970.7590 XPM28.95 KB

AKuP4XsJ…owbodNxQ

eca7e9c9642fd7…60ad06c07c2480

200 in → 1 out1045.2119 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.

7.443 × 10⁹⁴(95-digit number)

74439547954850620521…46735881612600709439

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

7.443 × 10⁹⁴(95-digit number)

74439547954850620521…46735881612600709439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.443 × 10⁹⁴(95-digit number)

74439547954850620521…46735881612600709441

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

1.488 × 10⁹⁵(96-digit number)

14887909590970124104…93471763225201418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.488 × 10⁹⁵(96-digit number)

14887909590970124104…93471763225201418881

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

2.977 × 10⁹⁵(96-digit number)

29775819181940248208…86943526450402837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.977 × 10⁹⁵(96-digit number)

29775819181940248208…86943526450402837761

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

5.955 × 10⁹⁵(96-digit number)

59551638363880496417…73887052900805675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.955 × 10⁹⁵(96-digit number)

59551638363880496417…73887052900805675521

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

1.191 × 10⁹⁶(97-digit number)

11910327672776099283…47774105801611351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.191 × 10⁹⁶(97-digit number)

11910327672776099283…47774105801611351041

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 #922,392

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