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Block #1,218,007

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2015, 3:37:27 AM Β· Difficulty 10.7253 Β· 5,588,902 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
473300f595a31c658a85356ef7e373f8eb02f6827b4252c4cf155dc87546ef03
View on Chainz β†—

Height

#1,218,007

Difficulty

10.725255

Transactions

1

Size

199 B

Version

2

Bits

0ab9aa50

Nonce

748,573,598

Timestamp

9/2/2015, 3:37:27 AM

Confirmations

5,588,902

Mined by

⛏️ P2SHALUDpg5V52AXUZHeFvEjtz492UnHDRNGFJ

Merkle Root

fefbbb394f5d155231595fd6de3fa95bed0fa71d9d56da16b3428f9f9dfbca30
Transactions (1)
Coinbasefefbbb394f5d15…428f9f9dfbca30
1 in β†’ 1 out8.6800 XPM109 B
ALUDpg5V…nHDRNGFJ
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.

4.146 Γ— 10⁹⁴(95-digit number)
41464849660611871311…16478276175362359519
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
4.146 Γ— 10⁹⁴(95-digit number)
41464849660611871311…16478276175362359519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.146 Γ— 10⁹⁴(95-digit number)
41464849660611871311…16478276175362359521
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
8.292 Γ— 10⁹⁴(95-digit number)
82929699321223742623…32956552350724719039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.292 Γ— 10⁹⁴(95-digit number)
82929699321223742623…32956552350724719041
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
1.658 Γ— 10⁹⁡(96-digit number)
16585939864244748524…65913104701449438079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.658 Γ— 10⁹⁡(96-digit number)
16585939864244748524…65913104701449438081
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
3.317 Γ— 10⁹⁡(96-digit number)
33171879728489497049…31826209402898876159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.317 Γ— 10⁹⁡(96-digit number)
33171879728489497049…31826209402898876161
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
6.634 Γ— 10⁹⁡(96-digit number)
66343759456978994098…63652418805797752319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.634 Γ— 10⁹⁡(96-digit number)
66343759456978994098…63652418805797752321
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:57,699,375 XPMΒ·at block #6,806,908 Β· updates every 60s
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