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Block #2,828,562

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2018, 9:50:09 AM Β· Difficulty 11.7119 Β· 4,011,696 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
267d28dbc4024b94ce3588821c76bcef6606da5597cd8b6036d132835e71beb1
View on Chainz β†—

Height

#2,828,562

Difficulty

11.711920

Transactions

1

Size

199 B

Version

2

Bits

0bb6405f

Nonce

862,331,205

Timestamp

9/7/2018, 9:50:09 AM

Confirmations

4,011,696

Mined by

⛏️ P2SHAXEjTQixjJRAjU4sJLkf7d6nAafqThguP2

Merkle Root

c73ccb727d92c2e7f5813cbe67c4a84ddb1cb1ce7da0fd98a43b08271e76660f
Transactions (1)
Coinbasec73ccb727d92c2…3b08271e76660f
1 in β†’ 1 out7.2800 XPM109 B
AXEjTQix…fqThguP2
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.

4.563 Γ— 10⁹⁡(96-digit number)
45633831299991627274…09655601150501778719
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
4.563 Γ— 10⁹⁡(96-digit number)
45633831299991627274…09655601150501778719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.563 Γ— 10⁹⁡(96-digit number)
45633831299991627274…09655601150501778721
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
9.126 Γ— 10⁹⁡(96-digit number)
91267662599983254549…19311202301003557439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.126 Γ— 10⁹⁡(96-digit number)
91267662599983254549…19311202301003557441
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
1.825 Γ— 10⁹⁢(97-digit number)
18253532519996650909…38622404602007114879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.825 Γ— 10⁹⁢(97-digit number)
18253532519996650909…38622404602007114881
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
3.650 Γ— 10⁹⁢(97-digit number)
36507065039993301819…77244809204014229759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.650 Γ— 10⁹⁢(97-digit number)
36507065039993301819…77244809204014229761
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
7.301 Γ— 10⁹⁢(97-digit number)
73014130079986603639…54489618408028459519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.301 Γ— 10⁹⁢(97-digit number)
73014130079986603639…54489618408028459521
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
1.460 Γ— 10⁹⁷(98-digit number)
14602826015997320727…08979236816056919039
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:57,966,377 XPMΒ·at block #6,840,257 Β· updates every 60s
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