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Block #2,434,409

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/21/2017, 3:59:38 PM Β· Difficulty 10.9176 Β· 4,405,562 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
01ad8830029064d77928c6cec0ce1c3985340bf714f102aa3e63ab8bb2dff58a
View on Chainz β†—

Height

#2,434,409

Difficulty

10.917590

Transactions

1

Size

199 B

Version

2

Bits

0aeae729

Nonce

1,919,038,541

Timestamp

12/21/2017, 3:59:38 PM

Confirmations

4,405,562

Mined by

⛏️ P2SHAZkUmp7HkuTBETQo3DXUK7LA3v8hqHVpgq

Merkle Root

47048b0502c92d59d10f26a9ed27868953a86b7883c85b049ac3bbd130423da7
Transactions (1)
Coinbase47048b0502c92d…c3bbd130423da7
1 in β†’ 1 out8.3800 XPM109 B
AZkUmp7H…8hqHVpgq
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.

1.879 Γ— 10⁹⁡(96-digit number)
18795127969554686657…16077955415655960319
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
1.879 Γ— 10⁹⁡(96-digit number)
18795127969554686657…16077955415655960319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.879 Γ— 10⁹⁡(96-digit number)
18795127969554686657…16077955415655960321
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
3.759 Γ— 10⁹⁡(96-digit number)
37590255939109373314…32155910831311920639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.759 Γ— 10⁹⁡(96-digit number)
37590255939109373314…32155910831311920641
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
7.518 Γ— 10⁹⁡(96-digit number)
75180511878218746628…64311821662623841279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.518 Γ— 10⁹⁡(96-digit number)
75180511878218746628…64311821662623841281
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
1.503 Γ— 10⁹⁢(97-digit number)
15036102375643749325…28623643325247682559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.503 Γ— 10⁹⁢(97-digit number)
15036102375643749325…28623643325247682561
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
3.007 Γ— 10⁹⁢(97-digit number)
30072204751287498651…57247286650495365119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.007 Γ— 10⁹⁢(97-digit number)
30072204751287498651…57247286650495365121
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:57,964,073 XPMΒ·at block #6,839,970 Β· updates every 60s
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