Block #1,453,949

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2016, 4:03:23 AM · Difficulty 10.7244 · 5,391,072 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08dbe90ab12b71c22ff45879f7f1a6cca9685d9de7787d7c8b507ebf47b0baf7

View on Chainz ↗

Height

#1,453,949

Difficulty

10.724368

Transactions

Size

1.90 KB

Version

Bits

0ab97028

Nonce

636,051,556

Timestamp

2/13/2016, 4:03:23 AM

Confirmations

5,391,072

Mined by

⛏️ P2SHASYzxn6scmhu1qmMQkq78h1b5j2zripFmr

Merkle Root

91af3fd7f45365dcd46c245092c7fa41354a4de7388ecf6fc3147aa067532407

Transactions (5)

Coinbased66177e615747f…1feeedb2e7af8e

1 in → 1 out8.7200 XPM109 B

ASYzxn6s…2zripFmr

f298a8cdd8ed41…b7b613bacce2bf

1 in → 2 out3575.7788 XPM227 B

AeGZ1Apc…Z6dDy7qA AHu1tiPi…xfnNonxQ

3114172a02232c…61ff079b1a60dd

2 in → 2 out1716.7076 XPM375 B

APUMWRik…Jj3edu87 ARxARkcm…sgHxLuZG

5e1a110ca3a534…54c3ac7a3bc447

2 in → 2 out0.6300 XPM373 B

AW1JVbVL…vyTpDGt9 AT6ULFrw…RG7Ei4Nf

2b347b08ed789c…a737ab943aad34

1 in → 18 out67.4897 XPM770 B

AT1oTbdU…zkY2kuSH AUQxZvLV…LH5WZHPT AUnk8ai6…8sUZxEZ5 AW6zRY4z…ELnj21DS AeELVCBs…cG79VPm3

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.

2.299 × 10⁹⁶(97-digit number)

22991404865149963023…56443974221182540799

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

2.299 × 10⁹⁶(97-digit number)

22991404865149963023…56443974221182540799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.299 × 10⁹⁶(97-digit number)

22991404865149963023…56443974221182540801

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

4.598 × 10⁹⁶(97-digit number)

45982809730299926047…12887948442365081599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.598 × 10⁹⁶(97-digit number)

45982809730299926047…12887948442365081601

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

9.196 × 10⁹⁶(97-digit number)

91965619460599852094…25775896884730163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.196 × 10⁹⁶(97-digit number)

91965619460599852094…25775896884730163201

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

1.839 × 10⁹⁷(98-digit number)

18393123892119970418…51551793769460326399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.839 × 10⁹⁷(98-digit number)

18393123892119970418…51551793769460326401

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

3.678 × 10⁹⁷(98-digit number)

36786247784239940837…03103587538920652799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.678 × 10⁹⁷(98-digit number)

36786247784239940837…03103587538920652801

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 #1,453,949

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