Block #1,226,972

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/8/2015, 6:14:42 AM · Difficulty 10.7348 · 5,574,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac7313577d6326df77615b42ccffea736cd6c9f583ed3a67d9be235cc7559841

View on Chainz ↗

Height

#1,226,972

Difficulty

10.734823

Transactions

Size

435 B

Version

Bits

0abc1d62

Nonce

84,650,055

Timestamp

9/8/2015, 6:14:42 AM

Confirmations

5,574,054

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

af06dc0fdf0af3c6e0266c7331a2507c3a365770919ba2abbdc6130fd04a1377

Transactions (2)

Coinbasef32a50a1143df0…245a533b2aaa89

1 in → 1 out8.6700 XPM116 B

AJCEY9yy…tg97E6zm

c7eddfa7776965…91baf406b2a851

1 in → 2 out8.6400 XPM227 B

AGGaaTtC…yaRMF9xh AcEGUXDj…JsRzHiLU

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.

1.295 × 10¹⁰⁰(101-digit number)

12957448159864652384…40904632361426943999

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

1.295 × 10¹⁰⁰(101-digit number)

12957448159864652384…40904632361426943999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.295 × 10¹⁰⁰(101-digit number)

12957448159864652384…40904632361426944001

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

2.591 × 10¹⁰⁰(101-digit number)

25914896319729304768…81809264722853887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.591 × 10¹⁰⁰(101-digit number)

25914896319729304768…81809264722853888001

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

5.182 × 10¹⁰⁰(101-digit number)

51829792639458609536…63618529445707775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.182 × 10¹⁰⁰(101-digit number)

51829792639458609536…63618529445707776001

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

1.036 × 10¹⁰¹(102-digit number)

10365958527891721907…27237058891415551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10¹⁰¹(102-digit number)

10365958527891721907…27237058891415552001

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

2.073 × 10¹⁰¹(102-digit number)

20731917055783443814…54474117782831103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.073 × 10¹⁰¹(102-digit number)

20731917055783443814…54474117782831104001

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