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Block #2,238,130

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2017, 2:04:03 PM Β· Difficulty 10.9461 Β· 4,602,445 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8cfe25689ed654f6fd56513c0567bc9074d3ca2bc684fbb905a2cf99a86a6b2
View on Chainz β†—

Height

#2,238,130

Difficulty

10.946107

Transactions

1

Size

200 B

Version

2

Bits

0af23414

Nonce

1,591,898,532

Timestamp

8/5/2017, 2:04:03 PM

Confirmations

4,602,445

Mined by

⛏️ P2SHAZtyyvxQG4tUs3syEUj7XoHfqcK5cE3tYC

Merkle Root

695a7eb27956a8165fcbeb4641ed16b573bc7f7c705471ba7b957300d92d5008
Transactions (1)
Coinbase695a7eb27956a8…957300d92d5008
1 in β†’ 1 out8.3300 XPM110 B
AZtyyvxQ…K5cE3tYC
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.

9.979 Γ— 10⁹⁴(95-digit number)
99796110849268006373…87445868212003700879
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
9.979 Γ— 10⁹⁴(95-digit number)
99796110849268006373…87445868212003700879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.979 Γ— 10⁹⁴(95-digit number)
99796110849268006373…87445868212003700881
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
1.995 Γ— 10⁹⁡(96-digit number)
19959222169853601274…74891736424007401759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.995 Γ— 10⁹⁡(96-digit number)
19959222169853601274…74891736424007401761
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
3.991 Γ— 10⁹⁡(96-digit number)
39918444339707202549…49783472848014803519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.991 Γ— 10⁹⁡(96-digit number)
39918444339707202549…49783472848014803521
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
7.983 Γ— 10⁹⁡(96-digit number)
79836888679414405098…99566945696029607039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.983 Γ— 10⁹⁡(96-digit number)
79836888679414405098…99566945696029607041
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
1.596 Γ— 10⁹⁢(97-digit number)
15967377735882881019…99133891392059214079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15967377735882881019…99133891392059214081
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:57,968,935 XPMΒ·at block #6,840,574 Β· updates every 60s
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