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Block #1,304,746

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2015, 6:13:47 AM Β· Difficulty 10.8527 Β· 5,538,241 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d64ae09b2b515135883cf100862e9fd7e21b07ecdc4622415dee692421eed86
View on Chainz β†—

Height

#1,304,746

Difficulty

10.852675

Transactions

2

Size

97.47 KB

Version

2

Bits

0ada48e6

Nonce

451,642,152

Timestamp

10/30/2015, 6:13:47 AM

Confirmations

5,538,241

Mined by

⛏️ P2SHAUBBkZbsQZvnGyckQBWXz6g8mBJE9Afr7p

Merkle Root

cea4c760076c35c1d8ac12ee3a5de92879d7bef239e421765e9dd6196099d06e
Transactions (2)
Coinbaseeb2a8e24e34bea…4f38f18ea240f4
1 in β†’ 1 out9.4800 XPM110 B
AUBBkZbs…JE9Afr7p
6299c2665fb484…9e4ad58e2983cb
873 in β†’ 2 out7501.1370 XPM97.27 KB
ARdVe6hk…QmgEA7NVAMo23iSa…GY7Wkb3L
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.218 Γ— 10⁹⁷(98-digit number)
12187890599524435943…97685649203037102079
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.218 Γ— 10⁹⁷(98-digit number)
12187890599524435943…97685649203037102079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.218 Γ— 10⁹⁷(98-digit number)
12187890599524435943…97685649203037102081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.437 Γ— 10⁹⁷(98-digit number)
24375781199048871887…95371298406074204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.437 Γ— 10⁹⁷(98-digit number)
24375781199048871887…95371298406074204161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.875 Γ— 10⁹⁷(98-digit number)
48751562398097743774…90742596812148408319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.875 Γ— 10⁹⁷(98-digit number)
48751562398097743774…90742596812148408321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
9.750 Γ— 10⁹⁷(98-digit number)
97503124796195487549…81485193624296816639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.750 Γ— 10⁹⁷(98-digit number)
97503124796195487549…81485193624296816641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.950 Γ— 10⁹⁸(99-digit number)
19500624959239097509…62970387248593633279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.950 Γ— 10⁹⁸(99-digit number)
19500624959239097509…62970387248593633281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.900 Γ— 10⁹⁸(99-digit number)
39001249918478195019…25940774497187266559
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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