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Block #2,871,432

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2018, 5:16:45 PM Β· Difficulty 11.6656 Β· 3,971,141 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4206e25b7aef1ea8568d3dc47d8957e1f9c4959e2880d8365337e34aaebe176a
View on Chainz β†—

Height

#2,871,432

Difficulty

11.665567

Transactions

1

Size

201 B

Version

2

Bits

0baa62a1

Nonce

60,443,683

Timestamp

10/7/2018, 5:16:45 PM

Confirmations

3,971,141

Mined by

⛏️ P2SHAYoiL951q6WhFcLGCgFEVgAASHw1gZUKer

Merkle Root

8d9b26036051c32bcf6c18e87d86186ed6b7a42d23bff440ac4a7f5a8013956c
Transactions (1)
Coinbase8d9b26036051c3…4a7f5a8013956c
1 in β†’ 1 out7.3400 XPM110 B
AYoiL951…w1gZUKer
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.

1.547 Γ— 10⁹⁢(97-digit number)
15479111120280812375…61779563168810926079
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
1.547 Γ— 10⁹⁢(97-digit number)
15479111120280812375…61779563168810926079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.547 Γ— 10⁹⁢(97-digit number)
15479111120280812375…61779563168810926081
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
3.095 Γ— 10⁹⁢(97-digit number)
30958222240561624750…23559126337621852159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.095 Γ— 10⁹⁢(97-digit number)
30958222240561624750…23559126337621852161
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
6.191 Γ— 10⁹⁢(97-digit number)
61916444481123249500…47118252675243704319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.191 Γ— 10⁹⁢(97-digit number)
61916444481123249500…47118252675243704321
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
1.238 Γ— 10⁹⁷(98-digit number)
12383288896224649900…94236505350487408639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.238 Γ— 10⁹⁷(98-digit number)
12383288896224649900…94236505350487408641
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
2.476 Γ— 10⁹⁷(98-digit number)
24766577792449299800…88473010700974817279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.476 Γ— 10⁹⁷(98-digit number)
24766577792449299800…88473010700974817281
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
4.953 Γ— 10⁹⁷(98-digit number)
49533155584898599600…76946021401949634559
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:57,985,011 XPMΒ·at block #6,842,572 Β· updates every 60s
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