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Block #2,916,548

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/9/2018, 10:05:46 PM Β· Difficulty 11.4320 Β· 3,925,837 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a274c03c44df062396776f5480e2c2f8ec15b334190cab7525487360e2838b80
View on Chainz β†—

Height

#2,916,548

Difficulty

11.432011

Transactions

2

Size

541 B

Version

2

Bits

0b6e9842

Nonce

285,891,405

Timestamp

11/9/2018, 10:05:46 PM

Confirmations

3,925,837

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

8ad6519d229681139ebab82514024bbb70277a486ab70bbf670aa1bd167662a2
Transactions (2)
Coinbaseec90951fc78059…282a955fcb6fee
1 in β†’ 1 out7.6500 XPM110 B
AbXwmGxD…4XXYP765
a1d4ee26be4492…c0d8fd0bee0bfd
2 in β†’ 2 out12.6600 XPM341 B
AeRAcqkS…N2QmbTQJAagzWnSn…4rGSNZYM
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.

2.442 Γ— 10⁹⁴(95-digit number)
24422490603646609072…58770232775254412479
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
2.442 Γ— 10⁹⁴(95-digit number)
24422490603646609072…58770232775254412479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.442 Γ— 10⁹⁴(95-digit number)
24422490603646609072…58770232775254412481
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
4.884 Γ— 10⁹⁴(95-digit number)
48844981207293218145…17540465550508824959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.884 Γ— 10⁹⁴(95-digit number)
48844981207293218145…17540465550508824961
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
9.768 Γ— 10⁹⁴(95-digit number)
97689962414586436291…35080931101017649919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.768 Γ— 10⁹⁴(95-digit number)
97689962414586436291…35080931101017649921
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
1.953 Γ— 10⁹⁡(96-digit number)
19537992482917287258…70161862202035299839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.953 Γ— 10⁹⁡(96-digit number)
19537992482917287258…70161862202035299841
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
3.907 Γ— 10⁹⁡(96-digit number)
39075984965834574516…40323724404070599679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.907 Γ— 10⁹⁡(96-digit number)
39075984965834574516…40323724404070599681
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
7.815 Γ— 10⁹⁡(96-digit number)
78151969931669149033…80647448808141199359
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:57,983,489 XPMΒ·at block #6,842,384 Β· updates every 60s
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