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Block #2,084,951

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/23/2017, 11:55:40 PM Β· Difficulty 10.8728 Β· 4,754,723 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5219ebe70357a7a8b0ed64ae724da1c83c25806a1b9f629dae8a40e8e4887d71
View on Chainz β†—

Height

#2,084,951

Difficulty

10.872834

Transactions

2

Size

1.11 KB

Version

2

Bits

0adf7209

Nonce

219,446,943

Timestamp

4/23/2017, 11:55:40 PM

Confirmations

4,754,723

Mined by

⛏️ P2SHAXq3kcFupDFxNZrM46iyiJQtnZTt8DeLyn

Merkle Root

fbea4a5aac59f62ffa423c1915b0d6ca84735cb2dbab4d2b7775b3b4c2d06b28
Transactions (2)
Coinbaseffa6a91685141f…669e6cafe0f14b
1 in β†’ 1 out8.4700 XPM109 B
AXq3kcFu…Tt8DeLyn
2d727e4f9bac64…c7c203ddac656b
6 in β†’ 1 out6074.7609 XPM935 B
ARNzgb5H…mvwhwExA
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.

3.394 Γ— 10⁹⁴(95-digit number)
33948852865119282984…61303735563572521599
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
3.394 Γ— 10⁹⁴(95-digit number)
33948852865119282984…61303735563572521599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.394 Γ— 10⁹⁴(95-digit number)
33948852865119282984…61303735563572521601
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
6.789 Γ— 10⁹⁴(95-digit number)
67897705730238565969…22607471127145043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.789 Γ— 10⁹⁴(95-digit number)
67897705730238565969…22607471127145043201
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
1.357 Γ— 10⁹⁡(96-digit number)
13579541146047713193…45214942254290086399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.357 Γ— 10⁹⁡(96-digit number)
13579541146047713193…45214942254290086401
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
2.715 Γ— 10⁹⁡(96-digit number)
27159082292095426387…90429884508580172799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.715 Γ— 10⁹⁡(96-digit number)
27159082292095426387…90429884508580172801
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
5.431 Γ— 10⁹⁡(96-digit number)
54318164584190852775…80859769017160345599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.431 Γ— 10⁹⁡(96-digit number)
54318164584190852775…80859769017160345601
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
1.086 Γ— 10⁹⁢(97-digit number)
10863632916838170555…61719538034320691199
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:57,961,681 XPMΒ·at block #6,839,673 Β· updates every 60s
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