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Block #144,606

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2013, 10:04:03 AM Β· Difficulty 9.8400 Β· 6,653,776 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c5af8a024efd720bb1ee5b161b2d59e0899fe9fea62edbce7e54b19373af0ff
View on Chainz β†—

Height

#144,606

Difficulty

9.839993

Transactions

2

Size

723 B

Version

2

Bits

09d709c0

Nonce

203,198

Timestamp

9/1/2013, 10:04:03 AM

Confirmations

6,653,776

Mined by

⛏️ P2SHAWuEP1fDpyJAi1RtaPGYMrKbpV5RPF1qec

Merkle Root

ac1c583b299e45baf5959f1c743ed8d3ed6d6bc02bd02775cd9c7d2c0c2c672f
Transactions (2)
Coinbasef7955545c4bdd7…395a04dd28af24
1 in β†’ 1 out10.3200 XPM109 B
AWuEP1fD…5RPF1qec
7d3aa7a7fd4b3f…f4b73a72bb7b5a
3 in β†’ 2 out20.1246 XPM523 B
AHkThtbx…wUmdMUZnAQbv3X6c…4py49WsE
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.

1.014 Γ— 10⁹⁷(98-digit number)
10143526783358860885…40056174880032787919
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
1.014 Γ— 10⁹⁷(98-digit number)
10143526783358860885…40056174880032787919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.014 Γ— 10⁹⁷(98-digit number)
10143526783358860885…40056174880032787921
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
2.028 Γ— 10⁹⁷(98-digit number)
20287053566717721771…80112349760065575839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.028 Γ— 10⁹⁷(98-digit number)
20287053566717721771…80112349760065575841
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
4.057 Γ— 10⁹⁷(98-digit number)
40574107133435443542…60224699520131151679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.057 Γ— 10⁹⁷(98-digit number)
40574107133435443542…60224699520131151681
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
8.114 Γ— 10⁹⁷(98-digit number)
81148214266870887085…20449399040262303359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.114 Γ— 10⁹⁷(98-digit number)
81148214266870887085…20449399040262303361
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
1.622 Γ— 10⁹⁸(99-digit number)
16229642853374177417…40898798080524606719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Circulating Supply:57,631,062 XPMΒ·at block #6,798,381 Β· updates every 60s
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