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Block #230,974

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/28/2013, 3:45:46 AM Β· Difficulty 9.9401 Β· 6,585,403 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d21b5e3515a17e70bfac2d26882c61296df4883afdc59b03614a377b0f88d504
View on Chainz β†—

Height

#230,974

Difficulty

9.940131

Transactions

1

Size

199 B

Version

2

Bits

09f0ac6f

Nonce

135,497

Timestamp

10/28/2013, 3:45:46 AM

Confirmations

6,585,403

Mined by

⛏️ P2SHAHuUFvcwFs1vESjXtQLYzFAMgcYLgfEVC7

Merkle Root

809b845210cabc93f3475c9cd1a9845e09cf7c5ba3023f4457c2280ba07af49b
Transactions (1)
Coinbase809b845210cabc…c2280ba07af49b
1 in β†’ 1 out10.1100 XPM109 B
AHuUFvcw…YLgfEVC7
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.

7.752 Γ— 10⁹³(94-digit number)
77527743182958844038…57726855074632012299
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
7.752 Γ— 10⁹³(94-digit number)
77527743182958844038…57726855074632012299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.752 Γ— 10⁹³(94-digit number)
77527743182958844038…57726855074632012301
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
1.550 Γ— 10⁹⁴(95-digit number)
15505548636591768807…15453710149264024599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.550 Γ— 10⁹⁴(95-digit number)
15505548636591768807…15453710149264024601
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
3.101 Γ— 10⁹⁴(95-digit number)
31011097273183537615…30907420298528049199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.101 Γ— 10⁹⁴(95-digit number)
31011097273183537615…30907420298528049201
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
6.202 Γ— 10⁹⁴(95-digit number)
62022194546367075230…61814840597056098399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.202 Γ— 10⁹⁴(95-digit number)
62022194546367075230…61814840597056098401
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
1.240 Γ— 10⁹⁡(96-digit number)
12404438909273415046…23629681194112196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.240 Γ— 10⁹⁡(96-digit number)
12404438909273415046…23629681194112196801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:57,775,144 XPMΒ·at block #6,816,376 Β· updates every 60s
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