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Block #3,127,527

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/6/2019, 12:37:26 PM Β· Difficulty 11.3250 Β· 3,716,227 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b799069c5510ca1957999ba9b6e4325ffab63336b0760b1c49245059c19573a1
View on Chainz β†—

Height

#3,127,527

Difficulty

11.324950

Transactions

2

Size

6.21 KB

Version

2

Bits

0b532ff4

Nonce

1,970,864,457

Timestamp

4/6/2019, 12:37:26 PM

Confirmations

3,716,227

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

89232ddad02da5d81202e9d4d6bdf582d71b6a006a908a0fc79261b6302cf97c
Transactions (2)
Coinbasebc45497dd16e6e…4dc215174ab14a
1 in β†’ 1 out7.8500 XPM110 B
AUMQRepm…tAfKmdW1
0ca7230169768e…3f52bf06652fa4
53 in β†’ 2 out411.7541 XPM6.01 KB
ATgjv9bW…5PDCqVRWAbXwmGxD…4XXYP765
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.

2.281 Γ— 10⁹⁴(95-digit number)
22818723009625375018…84308739091823919999
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
2.281 Γ— 10⁹⁴(95-digit number)
22818723009625375018…84308739091823919999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.281 Γ— 10⁹⁴(95-digit number)
22818723009625375018…84308739091823920001
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
4.563 Γ— 10⁹⁴(95-digit number)
45637446019250750037…68617478183647839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.563 Γ— 10⁹⁴(95-digit number)
45637446019250750037…68617478183647840001
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
9.127 Γ— 10⁹⁴(95-digit number)
91274892038501500074…37234956367295679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.127 Γ— 10⁹⁴(95-digit number)
91274892038501500074…37234956367295680001
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
1.825 Γ— 10⁹⁡(96-digit number)
18254978407700300014…74469912734591359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.825 Γ— 10⁹⁡(96-digit number)
18254978407700300014…74469912734591360001
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
3.650 Γ— 10⁹⁡(96-digit number)
36509956815400600029…48939825469182719999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.650 Γ— 10⁹⁡(96-digit number)
36509956815400600029…48939825469182720001
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
7.301 Γ— 10⁹⁡(96-digit number)
73019913630801200059…97879650938365439999
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:57,994,403 XPMΒ·at block #6,843,753 Β· updates every 60s
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