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Block #2,869,210

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/6/2018, 2:52:59 AM Β· Difficulty 11.6709 Β· 3,973,695 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f16ac4a153c04a851cca92ba9379d37f84e65b76de1f029359083691f96ba3d
View on Chainz β†—

Height

#2,869,210

Difficulty

11.670895

Transactions

2

Size

6.91 KB

Version

2

Bits

0babbfcb

Nonce

303,079,335

Timestamp

10/6/2018, 2:52:59 AM

Confirmations

3,973,695

Mined by

⛏️ P2SHARb2hZVhANMqBwinUvkc1u6wRj2f48WQCo

Merkle Root

9d3c179c03f4008e9130eaf9a4162c563b11a359403a94f40aca11c929ded259
Transactions (2)
Coinbase9c7e117efebe21…1261f47dcbd51c
1 in β†’ 1 out7.7800 XPM109 B
ARb2hZVh…2f48WQCo
5de56126aae8ed…f12b549d294095
46 in β†’ 2 out13286.0607 XPM6.71 KB
AT7R24XJ…gwCnPYp5AZTsBA8t…251CHQZq
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.

1.230 Γ— 10⁹⁢(97-digit number)
12305291475206378451…85512550341247037439
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
1.230 Γ— 10⁹⁢(97-digit number)
12305291475206378451…85512550341247037439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.230 Γ— 10⁹⁢(97-digit number)
12305291475206378451…85512550341247037441
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
2.461 Γ— 10⁹⁢(97-digit number)
24610582950412756902…71025100682494074879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.461 Γ— 10⁹⁢(97-digit number)
24610582950412756902…71025100682494074881
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
4.922 Γ— 10⁹⁢(97-digit number)
49221165900825513804…42050201364988149759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.922 Γ— 10⁹⁢(97-digit number)
49221165900825513804…42050201364988149761
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
9.844 Γ— 10⁹⁢(97-digit number)
98442331801651027608…84100402729976299519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.844 Γ— 10⁹⁢(97-digit number)
98442331801651027608…84100402729976299521
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
1.968 Γ— 10⁹⁷(98-digit number)
19688466360330205521…68200805459952599039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.968 Γ— 10⁹⁷(98-digit number)
19688466360330205521…68200805459952599041
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
3.937 Γ— 10⁹⁷(98-digit number)
39376932720660411043…36401610919905198079
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:57,987,587 XPMΒ·at block #6,842,904 Β· updates every 60s
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