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Block #2,633,873

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 3:47:06 PM Β· Difficulty 11.2126 Β· 4,208,929 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8a8dc688740870670f7fa63d3ccdd54610926ae0a3d3372c8042065fc091dbd
View on Chainz β†—

Height

#2,633,873

Difficulty

11.212649

Transactions

1

Size

201 B

Version

2

Bits

0b367023

Nonce

86,876,483

Timestamp

4/28/2018, 3:47:06 PM

Confirmations

4,208,929

Mined by

⛏️ P2SHALKGt7Y9PveDahMfxFCzopSgJExmsS6Wh1

Merkle Root

698d3b898b866580a8efe80819c2ce4f70b4662e0f483cb5a36a6d25b891bec1
Transactions (1)
Coinbase698d3b898b8665…6a6d25b891bec1
1 in β†’ 1 out7.9400 XPM110 B
ALKGt7Y9…xmsS6Wh1
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.

2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018559
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
2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018561
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
4.839 Γ— 10⁹⁢(97-digit number)
48393252831905341009…14394475017822037119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.839 Γ— 10⁹⁢(97-digit number)
48393252831905341009…14394475017822037121
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
9.678 Γ— 10⁹⁢(97-digit number)
96786505663810682018…28788950035644074239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.678 Γ— 10⁹⁢(97-digit number)
96786505663810682018…28788950035644074241
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
1.935 Γ— 10⁹⁷(98-digit number)
19357301132762136403…57577900071288148479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.935 Γ— 10⁹⁷(98-digit number)
19357301132762136403…57577900071288148481
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
3.871 Γ— 10⁹⁷(98-digit number)
38714602265524272807…15155800142576296959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.871 Γ— 10⁹⁷(98-digit number)
38714602265524272807…15155800142576296961
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
7.742 Γ— 10⁹⁷(98-digit number)
77429204531048545614…30311600285152593919
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:57,986,756 XPMΒ·at block #6,842,801 Β· updates every 60s
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