Block #922,303

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:02:05 AM · Difficulty 10.9158 · 5,884,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9ff767f93cb99ac5e62d5c34db1e92f22265dacba729953801449baf341ce07

View on Chainz ↗

Height

#922,303

Difficulty

10.915767

Transactions

Size

116.00 KB

Version

Bits

0aea6fb4

Nonce

553,268,008

Timestamp

2/4/2015, 9:02:05 AM

Confirmations

5,884,417

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d4cec2ebbd86a5679275e51a7a0727f17e588e7d1c740c882eb855ffdeaa002e

Transactions (5)

Coinbasee64dee147f006e…e1912d705c7d93

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

32093fd8dd50a3…fd94621b34d25e

200 in → 1 out1236.9659 XPM28.96 KB

AKuP4XsJ…owbodNxQ

dc1009ef8f75c4…16b100e5ece732

200 in → 1 out879.6999 XPM28.95 KB

AKuP4XsJ…owbodNxQ

7214dc8e54e504…1f885c695a4a34

200 in → 1 out988.6582 XPM28.95 KB

AKuP4XsJ…owbodNxQ

1d531ef0f68373…85a35905b9ac99

200 in → 1 out920.5134 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.

1.002 × 10⁹⁶(97-digit number)

10025426230869777410…33896266056862115839

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

1.002 × 10⁹⁶(97-digit number)

10025426230869777410…33896266056862115839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.002 × 10⁹⁶(97-digit number)

10025426230869777410…33896266056862115841

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

2.005 × 10⁹⁶(97-digit number)

20050852461739554821…67792532113724231679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.005 × 10⁹⁶(97-digit number)

20050852461739554821…67792532113724231681

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

4.010 × 10⁹⁶(97-digit number)

40101704923479109642…35585064227448463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.010 × 10⁹⁶(97-digit number)

40101704923479109642…35585064227448463361

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

8.020 × 10⁹⁶(97-digit number)

80203409846958219285…71170128454896926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.020 × 10⁹⁶(97-digit number)

80203409846958219285…71170128454896926721

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

1.604 × 10⁹⁷(98-digit number)

16040681969391643857…42340256909793853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.604 × 10⁹⁷(98-digit number)

16040681969391643857…42340256909793853441

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.208 × 10⁹⁷(98-digit number)

32081363938783287714…84680513819587706879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #922,303

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