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Block #241,483

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/3/2013, 5:58:05 AM Β· Difficulty 9.9579 Β· 6,601,691 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8c503ed79fa1142cef00f1d667705eaf517183cf48011f20e41d294a3a4a07f5
View on Chainz β†—

Height

#241,483

Difficulty

9.957947

Transactions

1

Size

199 B

Version

2

Bits

09f53c00

Nonce

80,515

Timestamp

11/3/2013, 5:58:05 AM

Confirmations

6,601,691

Mined by

⛏️ P2SHAUaEmySM5tjwy5MdAYvH6C99vGdHRUDBRZ

Merkle Root

47f5d02e9ba66ec7588d5252b25e01a01bdfce51af73061727d6bd22e68420e8
Transactions (1)
Coinbase47f5d02e9ba66e…d6bd22e68420e8
1 in β†’ 1 out10.0700 XPM109 B
AUaEmySM…dHRUDBRZ
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.

3.774 Γ— 10⁹⁴(95-digit number)
37748641441120210847…34557537977911138879
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
3.774 Γ— 10⁹⁴(95-digit number)
37748641441120210847…34557537977911138879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.774 Γ— 10⁹⁴(95-digit number)
37748641441120210847…34557537977911138881
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
7.549 Γ— 10⁹⁴(95-digit number)
75497282882240421694…69115075955822277759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.549 Γ— 10⁹⁴(95-digit number)
75497282882240421694…69115075955822277761
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
1.509 Γ— 10⁹⁡(96-digit number)
15099456576448084338…38230151911644555519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.509 Γ— 10⁹⁡(96-digit number)
15099456576448084338…38230151911644555521
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
3.019 Γ— 10⁹⁡(96-digit number)
30198913152896168677…76460303823289111039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.019 Γ— 10⁹⁡(96-digit number)
30198913152896168677…76460303823289111041
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
6.039 Γ— 10⁹⁡(96-digit number)
60397826305792337355…52920607646578222079
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:57,989,758 XPMΒ·at block #6,843,173 Β· updates every 60s
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