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Block #2,646,707

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 12:13:59 PM Β· Difficulty 11.7535 Β· 4,190,066 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e0a7e813b5d896958c76ecdee15ec702931eb9aaf9d402c2b2d92b62ee70f182
View on Chainz β†—

Height

#2,646,707

Difficulty

11.753451

Transactions

2

Size

427 B

Version

2

Bits

0bc0e223

Nonce

1,136,946,448

Timestamp

5/3/2018, 12:13:59 PM

Confirmations

4,190,066

Mined by

⛏️ P2SHAH7KqFscU3N7ybocYCNdGdxdEcxEyLkeQp

Merkle Root

3b91b42b3dfac6616af6fbcb3b1c3e1063ba710b3bc0cf0754a88e5283668d64
Transactions (2)
Coinbaseed3837c228e786…52704cb5bedd4b
1 in β†’ 1 out7.2400 XPM110 B
AH7KqFsc…xEyLkeQp
9785b6ea695829…84ff25889c6783
1 in β†’ 2 out47.4089 XPM227 B
AYcLEeK2…uy8rYsaWAZ4UnHzJ…PH7NQioA
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.

1.420 Γ— 10⁹⁡(96-digit number)
14206534417856551750…25376881639140395199
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
1.420 Γ— 10⁹⁡(96-digit number)
14206534417856551750…25376881639140395199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.420 Γ— 10⁹⁡(96-digit number)
14206534417856551750…25376881639140395201
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
2.841 Γ— 10⁹⁡(96-digit number)
28413068835713103500…50753763278280790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.841 Γ— 10⁹⁡(96-digit number)
28413068835713103500…50753763278280790401
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
5.682 Γ— 10⁹⁡(96-digit number)
56826137671426207001…01507526556561580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.682 Γ— 10⁹⁡(96-digit number)
56826137671426207001…01507526556561580801
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
1.136 Γ— 10⁹⁢(97-digit number)
11365227534285241400…03015053113123161599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.136 Γ— 10⁹⁢(97-digit number)
11365227534285241400…03015053113123161601
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
2.273 Γ— 10⁹⁢(97-digit number)
22730455068570482800…06030106226246323199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.273 Γ— 10⁹⁢(97-digit number)
22730455068570482800…06030106226246323201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.546 Γ— 10⁹⁢(97-digit number)
45460910137140965601…12060212452492646399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,938,461 XPMΒ·at block #6,836,772 Β· updates every 60s
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