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Block #2,726,969

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/29/2018, 5:16:43 PM Β· Difficulty 11.6277 Β· 4,114,937 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d01ddb8034a9b6bd4902df51aa50208497f7f7b6193afa7d462fa87dcc295bac
View on Chainz β†—

Height

#2,726,969

Difficulty

11.627664

Transactions

2

Size

1.68 KB

Version

2

Bits

0ba0ae95

Nonce

470,390,652

Timestamp

6/29/2018, 5:16:43 PM

Confirmations

4,114,937

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

e9c8a19d2cb1b25738fe88c8fcc2e726e3fa839e6109aa72053ea046473d38f2
Transactions (2)
Coinbasec3544c426f5f2e…f6b9aa8149a5b2
1 in β†’ 1 out7.4000 XPM110 B
AZtxQr2F…7grUWrUz
d9db4ca5dba2c5…13ac105db5aa44
10 in β†’ 1 out7.2861 XPM1.48 KB
ATwzU1WD…5JgyFF2d
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.

1.559 Γ— 10⁹⁢(97-digit number)
15598542438200051763…45320959220880983999
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
1.559 Γ— 10⁹⁢(97-digit number)
15598542438200051763…45320959220880983999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.559 Γ— 10⁹⁢(97-digit number)
15598542438200051763…45320959220880984001
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
3.119 Γ— 10⁹⁢(97-digit number)
31197084876400103527…90641918441761967999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.119 Γ— 10⁹⁢(97-digit number)
31197084876400103527…90641918441761968001
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
6.239 Γ— 10⁹⁢(97-digit number)
62394169752800207054…81283836883523935999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.239 Γ— 10⁹⁢(97-digit number)
62394169752800207054…81283836883523936001
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
1.247 Γ— 10⁹⁷(98-digit number)
12478833950560041410…62567673767047871999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.247 Γ— 10⁹⁷(98-digit number)
12478833950560041410…62567673767047872001
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
2.495 Γ— 10⁹⁷(98-digit number)
24957667901120082821…25135347534095743999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.495 Γ— 10⁹⁷(98-digit number)
24957667901120082821…25135347534095744001
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
4.991 Γ— 10⁹⁷(98-digit number)
49915335802240165643…50270695068191487999
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:57,979,622 XPMΒ·at block #6,841,905 Β· updates every 60s
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