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Block #2,067,776

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2017, 12:17:40 PM Β· Difficulty 10.8552 Β· 4,776,624 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e890a1a7f5a6b5bd17e33c2842d9f50b55c0cf9b80b3974df2b3ba81a49ea216
View on Chainz β†—

Height

#2,067,776

Difficulty

10.855225

Transactions

2

Size

4.61 KB

Version

2

Bits

0adaf00a

Nonce

969,020,783

Timestamp

4/12/2017, 12:17:40 PM

Confirmations

4,776,624

Mined by

⛏️ P2SHAG5cP6VcT3EwJYMknTAJVBLzT6C8hy72h4

Merkle Root

521f33ea733717c84e4740a41ab81d0c7242283dfbf26e6634c4be7d88bf5433
Transactions (2)
Coinbase30261e93cead4e…b476175588ea96
1 in β†’ 1 out8.5300 XPM109 B
AG5cP6Vc…C8hy72h4
0a89be6626d20f…9326145d49410c
30 in β†’ 2 out1715.2720 XPM4.41 KB
AFo1JApt…nj9Kd9LMAbjN3GdU…oBMaUL7z
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.

2.509 Γ— 10⁹⁴(95-digit number)
25090317919601227943…07163512648953143259
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
2.509 Γ— 10⁹⁴(95-digit number)
25090317919601227943…07163512648953143259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.509 Γ— 10⁹⁴(95-digit number)
25090317919601227943…07163512648953143261
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
5.018 Γ— 10⁹⁴(95-digit number)
50180635839202455886…14327025297906286519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.018 Γ— 10⁹⁴(95-digit number)
50180635839202455886…14327025297906286521
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
1.003 Γ— 10⁹⁡(96-digit number)
10036127167840491177…28654050595812573039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.003 Γ— 10⁹⁡(96-digit number)
10036127167840491177…28654050595812573041
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
2.007 Γ— 10⁹⁡(96-digit number)
20072254335680982354…57308101191625146079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.007 Γ— 10⁹⁡(96-digit number)
20072254335680982354…57308101191625146081
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
4.014 Γ— 10⁹⁡(96-digit number)
40144508671361964709…14616202383250292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.014 Γ— 10⁹⁡(96-digit number)
40144508671361964709…14616202383250292161
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:57,999,592 XPMΒ·at block #6,844,399 Β· updates every 60s
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