Block #1,123,257

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/22/2015, 11:31:09 PM · Difficulty 10.9386 · 5,694,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bb1b2f510e9d582715e12068eaf75450b542b366131fda56c1bd86772f28048

View on Chainz ↗

Height

#1,123,257

Difficulty

10.938643

Transactions

Size

2.27 KB

Version

Bits

0af04aeb

Nonce

627,129,931

Timestamp

6/22/2015, 11:31:09 PM

Confirmations

5,694,012

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

5d9a88eec3145ce537e203d52fd01e85a173ce489063b2bf9ed25085553ea75a

Transactions (3)

Coinbase7e95fc43a5edfa…5275593dbdc2fa

1 in → 1 out8.3700 XPM116 B

AJCEY9yy…tg97E6zm

0464e9efc49af4…1158b8c5cae69f

1 in → 51 out6.1361 XPM1.85 KB

AJ1kkxMb…s9mfTrKZ AXyoDB3P…gVR3fWfe AHwvQQUu…qiCnx3B1 AHCS331t…N8KPkBYk Ae79nBXQ…DJjQpLiN

40c732273d642f…fab675e1c34b41

1 in → 2 out2.7769 XPM226 B

AJuemSFP…yaN3VwJF AXourZrA…u89738dP

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.

1.233 × 10⁹⁷(98-digit number)

12339571218138071923…95724914766862547199

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

1.233 × 10⁹⁷(98-digit number)

12339571218138071923…95724914766862547199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.233 × 10⁹⁷(98-digit number)

12339571218138071923…95724914766862547201

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

2.467 × 10⁹⁷(98-digit number)

24679142436276143847…91449829533725094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.467 × 10⁹⁷(98-digit number)

24679142436276143847…91449829533725094401

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

4.935 × 10⁹⁷(98-digit number)

49358284872552287694…82899659067450188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.935 × 10⁹⁷(98-digit number)

49358284872552287694…82899659067450188801

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

9.871 × 10⁹⁷(98-digit number)

98716569745104575389…65799318134900377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.871 × 10⁹⁷(98-digit number)

98716569745104575389…65799318134900377601

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

1.974 × 10⁹⁸(99-digit number)

19743313949020915077…31598636269800755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.974 × 10⁹⁸(99-digit number)

19743313949020915077…31598636269800755201

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

3.948 × 10⁹⁸(99-digit number)

39486627898041830155…63197272539601510399

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 #1,123,257

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